Any point within a given Voronoi region is proximal to the data site (black point) associated with that region.
Notice how the highlighted region shrinks at each step. The algorithm never examines points outside the narrowing window. In a balanced tree with nnn points, this takes about log4(n)\log_4(n)log4(n) steps. For a million points, that's roughly 10 steps instead of a million comparisons.
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Yes, there's a built-in LED flashlight, with obligatory (and in my opinion, annoying) strobe and SOS modes.
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Why TV soap Hollyoaks is skipping a whole year